Square Root by Repeated Subtraction

The repeated subtraction method is an easier way that uses a special property of odd numbers. When you add up consecutive odd numbers, starting from 1, you always get a perfect square.

Using this property of consecutive odd numbers, we can check whether the given number is perfect square or not. To check for any number, we can use the following steps:

Step 1: Start with the given number.

Step 2: Subtract consecutive odd numbers.

Step 3: Count the number of times you subtract.

Step 4: The count is the square root.

Let’s illustrate this with an example:

Example: Find the square root of 81 by repeated subtraction.

Solution:

Start with the given number: 81.

Subtract consecutive odd numbers starting from 1 until reaching zero:

1. 81 − 1 = 80
2. 80 − 3 = 77
3. 77 − 5 = 72
4. 72 − 7 = 65
5. 65 − 9 = 56
6. 56 − 11 = 45
7. 45 − 13 = 32
8. 32 − 15 = 17
9. 17 − 17 = 0

Count the number of times you subtracted an odd number: 9.

The square root of 81 is the number of times you subtracted, which is 9.

So, the square root of 81 is 9.

Which is the Quickest Method?

Quickest method for prime factorization depends on the number you’re trying to factorize and personal preference. However, in many cases, using the repeated subtraction method can be quicker for smaller numbers, especially when you’re dealing with numbers that have small prime factors.

Square Root is the one of the many arithmetic operations in mathematics. Square root can be calculated using various methods in mathematics such as long division, prime factorization, repeated subtraction, etc. In this article, we will discuss methods of calculation of square root using prime factorization and repeated subtraction method.